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In a recent year, the rate of U.S. home ownership was 65.9%. Choose a random sample of 120 households across the United States. What is the probability that 65 to 85 (inclusive) of them live in homes that they own?
Intro Stats / AP Statistics
The Normal Distribution
The Normal Approximation to the Binomial Distribution
The Normal Distribution
Oregon State University
Idaho State University
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all right. Number 11 we have and equals 120 and P equals 65.9%. So that is 0.659 All right, so the mean is N times P. That's 100 20 times 200.659 and you should get 79.8 Okay, around to two decimals, if you need to. And for the standard deviation, we have the square root of NP, which we said was 79.8 Time's Hugh, which is the same as one minus p. All right. And on the calculator, you should get 5.19 Now, we want to know the probability that X is between 65 85. Inclusive. All right, so when we go to our conversion chart for less center equal to you, add 0.5 and you remove the equal sign, so 65 becomes 65.5. I'm sorry. Made a little mistake there. Let me just erase that. Okay? So X is greater than or equal to 65. Okay. When X is greater than or equal to you, subtract 0.5 and remove the equal sign. So 65 minus 0.5 is 64.5. Okay, and here we have X is less center, equal to and for less than or equal to you. Add 0.5 and you remove the equal sign. So 85 becomes 85.5 because you add 0.5. All right, so 85 becomes 85.5. You just add 0.5 and remove the equal sign. Okay, so 64.5 and 85.5 or the new X values and we have to do to Z scores doesn't matter which one is even water z two. So we'll start with 64.5 for the X value, minus the mean and divided by the standard deviation. That should give you a Z score of negative 2.81 And when you looked at up on the Z score table, you should get 0.25 Okay, When you get that, when you sulphur Z, you need to round to two decimal places because the table doesn't go beyond that. So for the other Z score, we're going to use X equals 85.5. All right. And again, minus the mean and divided by the standard deviation. Okay. And for this Z score, we should get one 0.24 And when you looked at up on the table, the Z score table. Look up. 1.24 You should get 0.89 25 Okay, now, you see, we have boundaries for X. All right, We have boundaries for X. So with these two probabilities, it lies in between these two. So we have to subtract them. All right. You can subtract and take the absolute value. Our just put the larger number first. So 0.89 to 5 minus 0.25 is going, Teoh. Equal 0.89 Okay. And when you convert that, 2% just move the decimal place over two places. All right? I guess since we had four desperate places, I'll make it 89.0%. All right, so basically the reason we have to subtract two numbers when you have the curve. Okay, you'll have one value here, and you'll have one value here, okay? And you're looking for the area in between those two values. All right? You're looking for the area in between the two value. So that's why we subtract them
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